When one derives rate equations which describe the kinetics of enzyme catalyzed reactions in the steady state and allow for the presence of all the reactants, one normally finds that the algebraic form of such equations with respect to the reactant concentrations differs with each different mechanism considered. The actin of inhibitors or activators also has different effects for different mechanism. Thus by determining the algebraic form of the rate equations, one can limit possible mechanisms and often deduce a unique kinetic mechanism. It has been the goal of this project to develop practical kinetic techniques for doing this and to use them to determine the kinetic mechanisms of selected enzymes. This approach has been very successful and the results from this project and from work done by others have shown that kinetic tools are among the most practical and powerful for studying enzymic mechanisms. All indications are that considerable development is still possible in the theoretical techniques, and of course the number of enzymes whose kinetic mechanisms are well worked out is still small.